Related papers: Energy localization and transfer in autoresonant w…
In this paper, using multiple scale analysis we derive a generalized mathematical model for amplitude evolution, and for calculating the energy exchange in resonant and near-resonant global triads consisting of weakly nonlinear internal…
We explore the energy transfer dynamics in an array of two chains of identical rigid interacting dipoles. A crossover between two different ground state (GS) equilibrium configurations is observed with varying distance between the two…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
We study spatial pattern formation and energy localization in the dynamics of an anharmonic chain with quadratic and quartic intersite potential subject to an optical, sinusoidally oscillating field and a weak damping. The zone-boundary…
We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one…
For understanding the dissipation in a rotating flow when resonance occurs, we study the rotating flow driven by the harmonic force in a periodic box. Both the linear and nonlinear regimes are studied. The various parameters such as the…
In a dissipationless linear lattice, spatial disorder or incommensurate modulation induce localization of the lattice eigenstates and block spreading of wave packets. Additionally, incommensurate arrays allow for the metal-insulator…
Autoresonance is a phase locking phenomenon occurring in nonlinear oscillatory system, which is forced by oscillating perturbation. Many physical applications of the autoresonance are known in nonlinear physics. The essence of the…
We theoretically demonstrate the concept of metadamping in dissipative metamaterials. We consider an infinite mass-spring chain with repeated local resonators and a statically equivalent periodic chain whose wave propagation characteristics…
We find a rich variety of counterintuitive features in the steady states of a qubit array coupled to a dissipative source and sink at two arbitrary sites, using a master equation approach. We show there are setups where increasing the pump…
We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total…
We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…
We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the…
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent…
We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve…
We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schr\"odinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We study the energy transfer in a classical dipole chain of $N$ interacting rigid rotating dipoles. The underlying high--dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their…
We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax…
System of differential equations describing the initial stage of the capture of oscillatory systems into the parametric autoresonance is considered. Of special interest are solutions whose amplitude increases without bound with time. The…